Question

Air enters a diffuser with velocity 150 m/s. The air has temperature 300 K and pressure 60 kPa. The air leaves the diffuser at 50 m/s. The efficiency of the diffuser is 70%. Model the air as an ideal gas with R = 287 J/kg-K, cP = 1005 J/kg-K, and cV = 717 J/kg-K. What is the temperature of the air leaving a reversible diffuser doing the same job (K)?

Answer 1

The temperature of the air leaving a reversible diffuser is 400 K.

Step-by-step explanation:

The temperature of the air leaving a reversible diffuser can be calculated using the efficiency of the diffuser. We can start by using the equation for the change in enthalpy:

ΔH = cp * (T2 - T1)

Where ΔH is the change in enthalpy, cp is the specific heat capacity at constant pressure, and T1 and T2 are the initial and final temperatures, respectively.

Given that the efficiency of the diffuser is 70%, we can also express the change in enthalpy as:

ΔH = efficiency * cp * (T1 - T0)

Where T0 is the temperature of the air entering the diffuser.

Solving for T2, we get:

T2 = T0 + (ΔH / (efficiency * cp))

Substituting the given values, we have:

T2 = 300 K + ((0.7 * 1005 J/kg-K * (150 m/s - 50 m/s)) / (0.7 * 1005 J/kg-K))

T2 = 300 K + 100 K

T2 = 400 K